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Characterization of q-solitons under trace conditions and conformal vector fields 迹条件和共形矢量场下q孤子的表征
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-10-10 DOI: 10.1016/j.bulsci.2025.103746
Antonio W. Cunha , Antonio N. Silva Jr. , Rahul Poddar
{"title":"Characterization of q-solitons under trace conditions and conformal vector fields","authors":"Antonio W. Cunha ,&nbsp;Antonio N. Silva Jr. ,&nbsp;Rahul Poddar","doi":"10.1016/j.bulsci.2025.103746","DOIUrl":"10.1016/j.bulsci.2025.103746","url":null,"abstract":"<div><div>We investigate gradient <em>q</em>-solitons <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> characterized by a non-positive or non-negative trace of the structure tensor <em>q</em>. Through the imposition of specific regularity conditions on the potential function <em>f</em>, we deduce that <em>M</em> is both stationary and <em>q</em>-flat, consequently rendering it trivial. In the non-gradient case, we assume a contracted Bianchi type condition and prove certain characterizations of <em>q</em>-solitons <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>X</mi><mo>)</mo></math></span> when the vector field <em>X</em> is conformal. Our results showcase versatility as we apply them to solitons associated with diverse geometric flows.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103746"},"PeriodicalIF":0.9,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Riemann surface foliations with non-discrete singular set 具有非离散奇异集的Riemann曲面叶理
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-10-02 DOI: 10.1016/j.bulsci.2025.103743
Sahil Gehlawat
{"title":"Riemann surface foliations with non-discrete singular set","authors":"Sahil Gehlawat","doi":"10.1016/j.bulsci.2025.103743","DOIUrl":"10.1016/j.bulsci.2025.103743","url":null,"abstract":"<div><div>Let <span><math><mi>F</mi></math></span> be a singular Riemann surface foliation on a complex manifold <em>M</em>, such that the singular set <span><math><mi>E</mi><mo>⊂</mo><mi>M</mi></math></span> is non-discrete. We study the behavior of the foliation near the singular set <em>E</em>, particularly focusing on singular points that admit invariant submanifolds (locally) passing through them. Our primary focus is on the singular points that are removable singularities for some proper subfoliation. The aim of this note is two-fold. First, we classify singular points based on the dimension of their invariant submanifold and, consequently, establish that for hyperbolic foliations <span><math><mi>F</mi></math></span>, the presence of such singularities ensures the continuity of the leafwise Poincaré metric on <span><math><mi>M</mi><mo>∖</mo><mi>E</mi></math></span>. Secondly, we look into the behavior of the leafwise Poincaré metric near the singular set. We prove that if a foliation is of transversal type in a sufficiently large set, then the modulus of uniformization map <em>η</em> is continuous on <em>M</em>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103743"},"PeriodicalIF":0.9,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sparkling saddle loops of vector fields on surfaces 表面上矢量场的闪亮鞍形环
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-29 DOI: 10.1016/j.bulsci.2025.103742
Ivan Shilin
{"title":"Sparkling saddle loops of vector fields on surfaces","authors":"Ivan Shilin","doi":"10.1016/j.bulsci.2025.103742","DOIUrl":"10.1016/j.bulsci.2025.103742","url":null,"abstract":"<div><div>We study bifurcations of vector fields on 2-manifolds with handles in generic one-parameter families unfolding vector fields with a separatrix loop of a hyperbolic saddle. These bifurcations can differ drastically from the analogous bifurcations on the sphere. The reason is that, on a surface, a free separatrix of a hyperbolic saddle may wind toward the separatrix loop of the same saddle. When this loop is broken, sparkling saddle loops emerge. In the orientable case, the parameter values corresponding to these loops form the endpoints of the gaps in a Cantor set contained within the bifurcation diagram. Due to the presence of a Cantor set, there is a countable set of topologically non-equivalent germs of bifurcation diagrams even in generic one-parameter families, in contrast to bifurcations on the sphere.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103742"},"PeriodicalIF":0.9,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global linear Cauchy problem 全局线性柯西问题
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-24 DOI: 10.1016/j.bulsci.2025.103740
Faiza Derrab
{"title":"Global linear Cauchy problem","authors":"Faiza Derrab","doi":"10.1016/j.bulsci.2025.103740","DOIUrl":"10.1016/j.bulsci.2025.103740","url":null,"abstract":"<div><div>This paper is devoted to the study of the Fuchsian Cauchy problem. We establish the global existence and uniqueness of a solution in spaces of functions of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>, <span><math><mi>k</mi><mo>∈</mo><mi>N</mi><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span>, with respect to the Fuchsian variable and entire with respect to the other variables. The method of proof is based on the application of the fixed point theorem in some Banach spaces defined by suitable majorant functions.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103740"},"PeriodicalIF":0.9,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145227282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The relation type of analytic and formal algebras 解析代数和形式代数的关系类型
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-18 DOI: 10.1016/j.bulsci.2025.103739
Maryam Akhavin, Abbas Nasrollah Nejad
{"title":"The relation type of analytic and formal algebras","authors":"Maryam Akhavin,&nbsp;Abbas Nasrollah Nejad","doi":"10.1016/j.bulsci.2025.103739","DOIUrl":"10.1016/j.bulsci.2025.103739","url":null,"abstract":"<div><div>We introduce the notion of relation types for analytic and formal <em>k</em>-algebras, extending a result by F. Planas-Vilanova to affine <em>k</em>-algebras. We establish the well-definedness and invariance of this notion by characterizing it in terms of André-Quillen homology and utilizing the Jacobi-Zariski long exact sequence of homology. In particular, we show that the relation type is an invariant of schemes of finite type over a field, analytic varieties, and algebroid varieties. We also provide a discussion and analysis of relation types for certain special varieties.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"205 ","pages":"Article 103739"},"PeriodicalIF":0.9,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Novel isoclasses of one-parameter exotic small quantum groups originating from a two-parameter framework 源自双参数框架的单参数奇异小量子群的新等类
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-16 DOI: 10.1016/j.bulsci.2025.103738
Naihong Hu , Xiao Xu
{"title":"Novel isoclasses of one-parameter exotic small quantum groups originating from a two-parameter framework","authors":"Naihong Hu ,&nbsp;Xiao Xu","doi":"10.1016/j.bulsci.2025.103738","DOIUrl":"10.1016/j.bulsci.2025.103738","url":null,"abstract":"<div><div>The classification of one-parameter small quantum groups remains a fascinating open problem. This paper uncovers a novel phenomenon: beyond the Lusztig small quantum groups—equipped with double group-like elements <span><span>[29]</span></span>—there exists a plethora of exotic small quantum groups, approximately fivefold more numerous than their standard counterparts, which originate from a two-parameter framework.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103738"},"PeriodicalIF":0.9,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hölder regularity of Hamilton-Jacobi cooperative systems with variable-order Caputo time derivative Hölder具有变阶Caputo时间导数的Hamilton-Jacobi合作系统的正则性
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-15 DOI: 10.1016/j.bulsci.2025.103737
Miguel Yangari
{"title":"Hölder regularity of Hamilton-Jacobi cooperative systems with variable-order Caputo time derivative","authors":"Miguel Yangari","doi":"10.1016/j.bulsci.2025.103737","DOIUrl":"10.1016/j.bulsci.2025.103737","url":null,"abstract":"<div><div>In this paper, we focus on parabolic cooperative systems where the standard time derivative is replaced by variable-order fractional derivatives of Caputo type. We study the well-posedness of solutions and also we establish results of Hölder regularity in time and space variables.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103737"},"PeriodicalIF":0.9,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A source identification problem for the bi-parabolic equation containing a poly-harmonic operator 含多谐算子的双抛物方程的源识别问题
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-12 DOI: 10.1016/j.bulsci.2025.103736
Dang Duc Trong , Bui Thanh Duy , Nguyen Dang Minh
{"title":"A source identification problem for the bi-parabolic equation containing a poly-harmonic operator","authors":"Dang Duc Trong ,&nbsp;Bui Thanh Duy ,&nbsp;Nguyen Dang Minh","doi":"10.1016/j.bulsci.2025.103736","DOIUrl":"10.1016/j.bulsci.2025.103736","url":null,"abstract":"<div><div>In this paper, we address the source identification problem for the bi-parabolic equation involving a operator. Specifically, we investigate the equation <span><math><msup><mrow><mo>(</mo><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>A</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>⋅</mo><mi>ψ</mi><mo>(</mo><mi>t</mi><mo>)</mo></math></span>, where <span><math><mi>A</mi></math></span> denotes a poly-harmonic operator. Given the perturbed data of <em>ψ</em> and <span><math><mi>u</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> (where <span><math><mi>T</mi><mo>&gt;</mo><mn>0</mn></math></span>), our objective is to determine <em>f</em>. Although several scientific publications have explored regularization techniques for bi-parabolic problems, the existing literature remains limited. By relaxing certain conditions on the function <em>ψ</em> and employing a truncation regularization method while considering the problem on an unbounded domain, we believe our results provide valuable insights.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103736"},"PeriodicalIF":0.9,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted majorization and improvements for Levinson and Ky Fan inequalities Levinson和Ky Fan不等式的加权多数化及其改进
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-11 DOI: 10.1016/j.bulsci.2025.103722
JinYan Miao
{"title":"Weighted majorization and improvements for Levinson and Ky Fan inequalities","authors":"JinYan Miao","doi":"10.1016/j.bulsci.2025.103722","DOIUrl":"10.1016/j.bulsci.2025.103722","url":null,"abstract":"<div><div>This article has four goals. First, integral majorization theory is largely generalized to several functions with different weights. Based on this tool, we improve Levinson inequality for 3-convex function, as consequences, some Ky Fan type inequalities can be unified and improved, 4-convex function can be slightly explored so that Ky Fan inequality is further refined under the view of higher-order convexity. Some more applications of the new majorization tool are also mentioned.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103722"},"PeriodicalIF":0.9,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complex symmetric weighted composition-differentiation operators on weighted Hardy spaces 加权Hardy空间上的复对称加权组合微分算子
IF 0.9 3区 数学
Bulletin des Sciences Mathematiques Pub Date : 2025-09-09 DOI: 10.1016/j.bulsci.2025.103735
Ching-On Lo, Anthony Wai-Keung Loh
{"title":"Complex symmetric weighted composition-differentiation operators on weighted Hardy spaces","authors":"Ching-On Lo,&nbsp;Anthony Wai-Keung Loh","doi":"10.1016/j.bulsci.2025.103735","DOIUrl":"10.1016/j.bulsci.2025.103735","url":null,"abstract":"<div><div>Complex symmetric weighted composition-differentiation operators on the weighted Hardy spaces <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>β</mi><mo>)</mo></math></span> with respect to the standard conjugation are investigated. Our results partially answer a question from a paper of Lim and Khoi (2018) <span><span>[12]</span></span> and subsume several existing ones in the literature. We also study the classes of self-adjoint, normal, co-isometric and unitary weighted composition-differentiation operators on <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>β</mi><mo>)</mo></math></span> as well as their relations with the property of complex symmetry.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"206 ","pages":"Article 103735"},"PeriodicalIF":0.9,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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